Research progress and prospect of silica-based polymer nanofluids in enhanced oil recovery

2.1 Blending method

The simplest technique to generate silica-based polymer NFs is to add nano-silica directly to the polymer. The addition of silica reduces adsorption on the rock and increases the polymer’s temperature and salt tolerance. Consequently, nano-silica-assisted polymer flooding has become a research hotspot in recent years [28,59].

Hu et al. [60] used AM, modified b-cyclodextrin (M-b-CD), and cetyl dimethyl allyl ammonium bromide (SD-16) to synthesize a new type of amine polyacrylamide polymer (ASM), and they studied the effect of silica on ASM. The viscosity of the composite increased with the increase in nano-silica concentration. In Figure 1, when the silica concentration is less than 0.6 wt%, silica NPs are adsorbed on the ASM. The silica NPs reached saturation state at a concentration of 0.6 wt%. And when the silica concentration is greater than 0.6 wt%, more silica NPs were connected by hydrogen bonds. The composites’ recovery rate increased from 6.56 to 10.08%, and their temperature tolerance, salt tolerance, and shear resistance were superior to those of ASM.

Figure 1

Illustration of the adsorption of nano-SiO₂ onto ASM chains for a fixed ASM concentration: (a) nano-SiO₂ attached to ASM chains via hydrogen bonds, (b) saturated state (all the sites attached by nano-SiO₂), and (c) nano-SiO₂ bridging in the network [60].

Furthermore, Yousefvand and Jafari [61] discovered that the addition of silica NPs increased scanning efficiency and improved the oil recovery rate in a NaCl/HPAM/SDS solution at 3.0 wt% sodium chloride, 0.5 wt% SiO₂, and 0.08 wt% hydrophobically conjugated polyacrylamide (HPAM). Kumar et al. [62] studied the oil samples with a heavy oil density of 973 kg/m³ and an average molecular weight (MW) of 12.0 × 10⁶ HPAM and discovered that 1.7 wt% nano-silica EOR was the highest and increased by 8.3% compared with HPAM. Kumar et al. [63] finally optimized 5.0 wt% polyethylene glycol and 0.04 wt% silica, which resulted in the optimum emulsion stability and recovery of 27.82%.

Low-salinity water injection (LSW) is an efficient and environmentally friendly oil recovery method [64–66]. Behera and Sangwai [67] prepared LSW injection from seawater with a conductivity of 0.055 μS/cm and a resistivity of 18.2 MΩ cm. Anionic surfactant was added into LSW, and then nano-silica was added for ultrasonic treatment for some time. Finally, polymer PVP-K30 was added for homogenization to obtain new mixed NFs [68,69]. The water injection effect of NFs was greater than that of LSW injection.

In terms of biopolymers, xanthan gum is a microbial polysaccharide widely used in EOR [70]. Kennedy et al. [71] mixed silica NPs with distilled water until entirely dissolved. The xanthan gum was then added at 45°C and mixed until the xanthan gum completely dissolved. Finally, a particle-dispersed polymer was obtained. Nano-silicon dioxide was spread out in the solution in a pretty even way, and the adsorption capacity was lowered [72]. Moreover, when adding 1.0 wt% silica NP, the guar polymer EOR was 44.28% [73]. Soliman et al. [74] showed that adding modified NPs to xanthan gum and scleroglucan improved their rheological properties and enhanced their temperature and salt tolerance.

The addition of silica to the polymer increases the viscosity of the polymer solution to a certain extent. But Zeyghami et al. [75] put forward different views on the effect of adding nano-silica to the polyacrylamide polymer solution. They proposed that adding silica particles into the solution would interact with the polyacrylamide polymer. It may even lead to a decrease in viscosity. The blending method is the easiest, but nano-silica tends to aggregate, especially with the addition of electrolytes [75,76]. In the presence of electrolytes, flocculation will also occur. Consequently, the surface modification of nano-silica is usually carried out with a silane coupling agent [77,78]. Table 1 shows some research results of silica-based polymer NFs prepared by the blending method.

2.2 Grafting to method

The “grafting to” method introduces active groups on the surface of silica and directly grafts the polymer containing functional end groups onto the surface of silica [79,80]. To obtain particular organic function and pore structure [81,82], many parameters need to be improved, such as silane molar ratio, temperature, and pH [83,84]. Notably, the synthesis of polymers was highly dependent on the properties and positions of organic functions [85].

Tsubokawa and Yoshikawa [86] introduced an amino group into the silica surface, and poly MeOZO was grafted onto the silica surface to obtain the hyperbranched polymer graft of silica. Due to the steric hindrance of silica increasing with the MW of the functional polymer, the grafting ratio was affected by the MW of the functional polymer.

Sun et al. [87] added HPAM powder to the silica suspension, and the concentration was maintained at 2.0%. Then, chromium acetate was added dropwise to the suspension, and the concentration of the cross-linking agent was maintained at 0.2%. Finally, they synthesized the nanocomposite gel with an optimum nano-silicon content of 10%. The adsorption of nano-silica particles around polymer chains resulted in a three-dimensional network structure with good mechanical characteristics.

Daneshmand et al. [88] prepared functionalized polyethylene glycol methyl ethers using acetic acid catalysis of polyethylene glycol ether and 3-glycidoxypropyltrimethoxysilane (GPTMS) (Figure 2a). C3S was added to a 5 wt% silica solution to obtain C3S grafted silica (Figure 2b). The mixed polyethylene glycol methyl ether/C3S-containing silica was synthesized at 80°C and pH = 9.5.

Figure 2

Chemical reaction steps: (a) the functionalized polyethylene glycol methyl ether by GPTMS, (b) the modified silica by trimethoxy (propyl) silane (C3S), and (c) the addition of functionalized polyethylene glycol methyl ether on the surface of the modified silica with C3S [88].

2.3 Grafting from method

The “grafting from” method is to obtain polymer by polycondensation of active end groups introduced by nano-silica and monomers [79]. Polymers are commonly synthesized using free radical polymerization and surface-initiated atom transfer radical polymerization in this approach [6]. In general, silane coupling agents and epoxy compounds are used to modify the surface of silica [89–91]. The amount of hydroxyl on the surface of nano-silica changed with the dosage of the silane coupling agent [92]. Maleic anhydride (MAH) interacted with modified silica to produce surface modification of nano-SiO₂ (SMNS), according to Lai et al. [93]. Finally, high branched polymers (acrylic acid (AA)/AM/SMNS) synthesized by free radical polymerization of AA, AM, and SMNS. Its microstructure was dense, and had an excellent matching relationship with pore throat. In the reservoir with a permeability of 300 mD, the recovery rate of 1,500 mg/L polymer was 15.47%.

Yang-Chuan et al. [94] dissolved SDS in an AM solution and added styrene to form the emulsion. In addition, 2-methyl-2-[(1-oxo-2-propenyl)amino]-1-propanesulfonic acid (AMPS) was added to the reaction solution, and modified silica (SiO₂-MPS) was added after 30 min of nitrogen flow to prepare PA-B-S nanocomposites. Experiments revealed that PA-B-S nanocomposites could be used to extract heavy oil from low permeability reservoirs. Hu et al. [92] also used cryloxypropyltrimethoxysilane (MPS) to modify silica and introduced b-CD into the polymer chain to enhance the temperature and salt tolerance of the polymer. AAMC-S1 nanocomposites were prepared by free radical copolymerization using AM, AMPS, MAH-b-CD, and SiO₂-MPS. Furthermore, Maurya et al. [95] designed silica-MPS with γ-MPS modification. polyacrylamide grafted silica particles PAAGS was synthesized by free radical polymerization with Silica-MPS and AM using the initiator 2,2'-Azobis(2-methylpropionitrile) (AIBN). Besides that, Liu et al. [96] synthesized star-like polymer (SLP) NPs by water-free radical polymerization using AA, AMPS, AM, and functional groups-terminated NPs (FNPs) [97]. Meanwhile, polymer SLPs with different MWs were prepared by controlling the mass feed of 2,2-azobis(2-amidinopropane) dihydrochloride (AIBA).

As shown in Figure 3, Liu et al. [98] synthesized hydrophobic monomer MeDiC₈AM and then used MAH functionalized silica to obtain FNPs. Afterward, AA, AM, FNPs, and MeDiC₈AM were added to the mixture to synthesize a novel star-like hydrophobically conjugated polyacrylamide (SHPAM) with a nano-silica core and amphiphilic chain polymerization.

Figure 3

Synthesis method of SHPAM [98]. (a) MeDiC₈AM, (b) FNPs (diameter of 30 nm), and (c) SHPAM.

Ye et al. [50] used vinyltriethoxysilane (VTES) and silica to prepare NSFM. The AM/AA/NSFM copolymer was prepared by AA, AM, NSFM, and NaHSO₃-(NH₄)₂S₂O₈ as initiators. In addition, AM/AA copolymer was synthesized by the same method. AM/AA/NSFM copolymer performed better in terms of temperature tolerance, shear resistance, and oil displacement ability. Hayashi et al. [99] used 4-cyanopentanoic acid to introduce azo groups into silica, which they then reacted with amino groups on the monomer to produce hyperbranched polymers. The most popular Grafting from method for creating silicon-based polymer NFs are listed in Table 2.

3.1 Rheological property

Rheology is the basis of the design and evaluation of oil displacement, and it is critical in determining the optimal concentration of injection [100,101]. Flow ratio (M) refers to the flow ratio of the displacement phase to displaced phase [102]. Controlling the flow rate is of great significance in improving the macro displacement efficiency [103]. The viscosity of the displacement agent can be increased by improving rheology. Viscosity represents the friction caused by the movement of the inner liquid layer, which is related to the aggregation of polymer molecules [104]. The recovery factor was mainly improved by increasing the viscosity of the polymer in the applications [105,106]. In addition to the injection process and the environmental factors of the polymer solution, the method of increasing the viscosity of the polymer is mainly to introduce the monomer and increase the relative molecular mass of the polymer. However, the high viscosity of the polymer is not conducive to the injection of polymer solution, and the cost is also a big problem [107].

The goal of enhanced oil recovery is that the ratio of displacement phase mobility to displaced phase mobility (Mr) is less than one [100]. Polymers such as HPAM could increase the viscosity of displacement fluid, thereby reducing mobility [108]. However, under high temperatures and salinity, the recovery was reduced due to the increase in fluidity of the polymer chain. In order to alleviate the above problems, mobility control could be achieved by nano-composite materials formed by silica and polymer [109,110]. Nano-silica composites prepared by graft copolymerization of modified nano-silica with octadecyl methacrylate, styrene, MAH, and acrylamide reduced the viscosity of heavy oil by more than 60% and enhanced its mobility [111–113].

The addition of nano-silica modified the rheological properties of the polymer and improved its elastic efficiency and shear resistance [48,114,115]. In addition, the viscosity of the polymer increased with the addition of silica [116–118]. For example, the viscosity of guar gum solution increased significantly with the increase in silica NP concentration [73]. The apparent viscosity of the PAAM-SNP polymer solution increased as the polymer concentration increased. Furthermore, the viscosity increased more significantly when the concentration was greater than the critical association concentration (about 0.125% w/w) [119].

In their research of viscosity-enhancing mechanisms, Maurya and Mandal [120] found silica was a physical crosslinking agent. In Figure 4(a), the polyacrylamide suspension polymer chain was adsorbed on the surface of sodium silica, forming a flocculation structure. The formed macromolecular structure was very stable due to irreversible adsorption, increasing the viscosity. In Figure 4(b), at low concentrations, the viscosity increment of the three-dimensional network was greater than the viscosity reduction due to polymer adsorption. Nano-silica/polyacrylamide suspensions had strong interactions due to the formation of hydrogen bonds. Hu et al. [60] studied ASM/SiO₂ and concluded that Si-OH and-CO-NH₂ formed hydrogen bonds, which enhanced the three-dimensional network structure. The host–guest inclusion complex formed by hydrophobic molecules created a three-dimensional network structure, which increased viscosity.

Figure 4

(a) Mechanism of irreversible bridging of silica particles through adsorption of PAM on silica surface. (b) Effect of polymer concentration on degree of bridging of silica particle in silica/PAM suspension [120].

The viscosity of the polymer solution decreased with the increase in shear rate. At a high shear rate, the viscosity of the polymer solution decreased, and the curves of viscosity were in line with the power-law fluid formula. But silica-based polymer NFs increased the shear resistance compared with polymers. Because of the nucleation effect of silane groups, the network structure strength of SiO₂ polyacrylate composite material increased. As a result, shearing only destroys part of the branched chain, and shearing has no noticeable impact on the polymer [121].

The mechanism by which nano-silica improves polymer tolerance in harsh environments is being investigated. The mobility of PAM molecules increases at high temperatures, reducing the intermolecular interaction of PAM polymer macromolecules. Heating reduced the binding between polymer molecules and even destroyed molecular chains. The crosslinking effect of silica at high temperatures provides the polymer with good rheology [94]. Because of the adsorption, the polymer in the silica/PAM suspension formed a three-dimensional micelle network. In addition to the formation of hydrogen bonds, SNP provided spatial steric hindrance and reduced the coiling of molecular chains, which improved the temperature tolerance of PAM/SNP. At 90°C, the viscosity of pure PAAM solution was only half of PAM/SNP [120]. In the salt environment, the polymer is degraded and the viscosity is reduced. However, the ion-dipole interaction between NPs and cations minimized the degradation of the polymer [122]. The shielding effect reduced the attack of divalent ions on polymer chains while having little effect on viscosity under harsh conditions. In addition, hydrogen bonds enhanced the polymer network to resist high ionic strength [98]. Moreover, silica particles prevent the polymer from curling due to nucleation through bridging, resulting in a tighter polymer network [123]. Necessarily, the presence of electrolytes reduced the viscosity of silica-based polymers, so it was particularly essential to modify the surface of silica [75].

However, Cao et al. [104] demonstrated that using flow ratio and viscosity to evaluate recovery factors was illogical. Regardless of the polymer’s viscosity, the recovery efficiency can be enhanced by placing silica-based polymer NFs in a high-permeability layer. Xiangguo et al. [124] further pointed out that the viscosity of silica-based polymer NFs was not positively correlated with the oil displacement effect. The compatibility between the silica-based polymer NFs and the reservoir, and the retention and migration ability of the silica-based polymer NFs were essential factors in improving the swept volume.

3.2 Wettability

Wettability is an important surface property that reflects the trend of preferential contact with a fluid in the fluid system [125,126]. Moreover, wettability is an essential factor affecting fluid distribution and oil recovery in porous media [127]. Surface wettability is usually characterized by contact angle [128]. The angle of the droplet at the three-phase interface of solid–liquid–gas is measured by the static droplet method [129]. Because it is easy to operate, it is the most commonly used contact angle measurement method. But this method is suitable for measuring ideal and smooth planes [130]. It can be classified as water-wet (hydrophilic), oil-wet (hydrophobic), or neutral based on the contact angle (less than 90°, greater than 90°, or equal to 90°) [131]. Hydrophilicity or lipophilicity depends on the chemical composition of the fluid, which affects the molecular attraction [132,133]. The impacts on the attractiveness of molecules include reservoir rock mineral composition and properties, adsorption or desorption of fluid components on the surface, spread ability of oil phases, and temperature [134,135].

Nano-silica has been discovered to be an effective wetting agent by releasing carboxylic acid groups from the oil-wet surface, thereby changing the hydrophobic to hydrophilic nature of the rock surface [136]. According to Lu et al., the adsorption of nano-silica on the rock surface increased wettability, and the recovery rate could reach 20.68% [137]. Hydrophilic changes on the surface can be achieved by inorganic ions and surfactants with hydrophilic groups [138,139]. As a result, the oil displacement agent with wettability consists primarily of LSW flooding, surfactant, and NP fluid. After surface active polymer flooding, the contact angle of reservoir rock decreases and the reservoir rock becomes hydrophilic [140,141].

Omran et al. [142] established a microfluidic chip with a permeability of 2.5 to investigate the effects of wettability on oil recovery. As a result, the polymer-coated silica nanoparticles (PSiNPs) improved the oil recovery performance compared to the synthetic seawater in the three wetting conditions (water-wet, intermediate-wet, and oil-wet). PSiNPs EOR of IOIP (Initial oil in place) reached 88.1% under water wetting, which was better than that under medium or oil wetting. At the same time, PSiNPs controlled the invasion of areas not affected by the displacement front.

Maghzi et al. [143] used polyacrylamide solution and dispersed silica nanoparticles (DSNP) in polyacrylamide to explore the effect of SNPs on oil recovery. As shown in Figure 5, DSNP could remove oil from the pore wall and throat wall, reducing residual oil. However, polyacrylamide solutions are incapable of removing oil from the pore and throat walls. The hydrophilicity of SNPs with a diameter of 14 nm changed the micro-model from oil to water. Finally, the recovery of DSNP was 10% higher than that of polyacrylamide solution.

Figure 5

Pore scale visualization of wettability, oil (brown), and solution (white): (a) oil films on the wall of throats show an oil-wet porous medium, (b) trapped polymers in pores and throats show an oil-wet porous medium, (c) partial remained oil due to incomplete silica adsorption onto medium surface, (d) absence of oil films shows water-wetting property in throats after DSNP solution flooding [143].

Luo et al. [144] showed that the contact angle between the oil phase and core was 6°, indicating that the initial tight carbonate was lipophilic. The contact angle gradually increased as the concentration of polymer encapsulated silica nanoparticles (CM-NP) increased. When the concentration was 0.5 wt%, the contact angle was 75°. Furthermore, the contact angle was 124° when the concentration was 2.0 wt%. Therefore, the surface gradually changed from lipophilic to hydrophilic with the increase in concentration.

Bila et al. [25] investigated the EOR mechanism using four spherical silica NPs with different particle sizes (32, 107, 145, and 218 nm) and their surface functionalized with polymer molecules. The recovery rate ranges from 7 to 14%, demonstrating that the recovery mechanism is caused by a decrease in interfacial tension (IFT) and a change in wettability, while the porosity and permeability of rocks are affected by particle size.

Behzadi and Mohammadi [52] aged oil-wet glass slides in 1 wt % surface-modified silica nanofluids first. After 72 h, the droplet contact angle was measured . It was observed that the contact angle of the carbonate section decreased. One mechanism was that the negative ether group in the polyethylene glycol chain on the silica surface interacted electrostatically with Ca²⁺ in the carbonate, which enhanced the hydrophilicity of the carbonate. Another mechanism was the electrostatic interaction between the positive side of the asphalt band and the negative ether group. In addition, hydrophilic or environmentally sensitive silica NFs had a faster rate of contact angle decay.

To understand the significance of reservoir wettability types, it is necessary to investigate the capillary number, CDC curve, and phase capture. In limestone experiment, the porous medium was modeled as capillary, and the protective phase existed in the form of annular membrane. In the water-wet state, the experiment demonstrated that the capillary force decreased and the oil phase permeability increased, which was conducive to oil displacement [145]. The Janus-GONs could convert the oil-wet carbonate samples to completely mixed moisture, while silica altered the wettability of the same sample to be partially water-wet. This change could be attributed to NP adsorption [146]. However, some studies have shown that further oil will be recovered if the wettability changes from water-wet to mixed-wet [131,147]. Therefore, in equation (1), we defined the ratio of viscous force to capillary force as capillary number [146]. According to equation (1), the more the capillary number is, the greater the recovery. Therefore, it should be noted that the more NPs make a surface water-wet, the less oil will be obtained. But adjusting the wettability of the medium to intermediate conditions will greatly improve the oil recovery rate [146].

where μ D is the displacing fluid viscosity (cp), ϑ Inj is the flow velocity (m/s), σ ow is the oil–water IFT (mN/m), and θ is the contact angle (degree).

It was generally believed that the capillary desaturation curve (CDC) reflected the characteristics and arrangement of the pores and the distribution of fluid in the pores [148]. Classical CDC demonstrated that the higher the capillary number, the lower the residual oil saturation. CDC deviates from the typical CDC shape under mixed humidity and water humidity conditions, and residual oil saturation may increase or decrease with the increase in capillary number [149]. In addition, wettability was the main factor controlling phase trapping, and different wettability distributions led to different trapping modes [150,151]. Tanino and Blunt [152] pointed out that the increased coordination of several throats contributed to the capture of protective fluids.

Furthermore, Bila et al. [153] pointed out that NPs were fixed on the wedge formed between the three-phase contact lines of water-oil-rock under the water-wet conditions, resulting in additional separation pressure. Wasan and Nikolov [154] proposed that dipole–dipole interaction would also cause attraction. Despite the fact that there were numerous mechanisms, the mechanism of surface wettability change remained complex.

3.3 Interfacial tension

The dynamic method measured interfacial tension directly [155]. Tylor proposed the equation for the evolution of micro-deformation droplet shape as follows [156]:

where D is the drop deformation parameter defined as D = ( L − B ) ( L + B ) , L is the major axis of ellipsoidal drop, and B is the minor. D 0 is the initial value of deformation parameter, σ is the interfacial tension, p is the viscosity ratio of the dispersed droplet to the matrix, η m is the viscosity of matrix, R 0 is the equilibrium radius of sphere drop, and t is the time of retraction.

Many published reports have shown that when the MW of the polymer is less than its entangled MW, the interfacial tension of the polymer increases with the increase in MW [157–159]. Pan et al. [160] discovered that the interfacial tension of polystyrene/polypropylene blends decreased linearly as temperature increased in a specific range. More importantly, Sheng stated that lowering IFT to 10⁻³ mN/m will significantly improve recovery [161]. The interfacial tension of polymers with surface activity decreases with increasing concentration, but it cannot reach ultra-low interfacial tension [141]. Nevertheless, even at no less than 10⁻³ mN/m, the reduction in IFT still played an essential role in enhancing the oil recovery. Although reducing the interfacial tension is not the main mechanism for improving the oil recovery rate of the surfactant polymer, the interfacial tension plays an important role in the polymer morphology and oil displacement effect [162,163]. In addition, the experiment demonstrated that nano-silica reduced the interfacial tension of two-phase systems and improved oil recovery [164]. Usually, SiO₂ is designed to be two-phase wet to reduce IFT better [165].

Mo et al. [166] measured two-dimensional space simultaneously through ellipsoidal droplets with zero inclination. There were already accurate methods for measuring interfacial tension [167,168]. Behzadi and Mohammadi [52] studied SNPs coated with polyethylene glycol and propylene chains. The results showed that the interaction between polyethylene and oil phase was strong, and the interaction between polyethylene glycol and water was strong. Maurya et al. [95] showed that PAAGS reduced surface tension and interfacial tension compared to silica. The lowest interfacial tension of PAAGS was about 8 mN/m at 1,200 ppm. This was because the grafted polymer made the size of PAAGS larger and improved the surface activity of PAAGS [169]. On the other hand, the specific surface area of the silica adsorbed on the surface increased and the hydrophilicity enhanced, so that the PAAGS better covered the oil–water interface [170]. A decrease in interfacial tension and surface tension in PAAGS improved the recovery efficiency to some extent, and low IFT also helped to change the wettability of rock.

Bila and Torsæter [28] concluded that the size of NPs affected the decrease in interfacial tension. When the size was 32 nm, the interfacial tension decreased by 71.8%. This was caused by the nano-silica’s strong adsorption capacity and small size at the interface. It was also possible that the repulsion between the polymer and the SNPs increased, increasing the separation pressure [171]. In addition, the decrease in interfacial tension of polymer coated silica particles may be due to the stability of NPs suspension. However, the high temperature had adverse effects on interface function.

As presented in Figure 6, Saha et al. [172] explored the factors affecting the interfacial tension. IFT of xanthan gum was 17.8 mN/m at 5,000 ppm and 30°C. With the increase in SNPs concentration, IFT of the xanthan gum system assisted by SNPs decreased, and IFT stabilized at 0.3 wt%. At 0.3 wt%, the IFT decreased by about 1.8 mN/m at 70°C when compared to 30°C. Hydrophilic and hydrophobic interactions between oil and water interfaces were also reasons for the decrease in IFT. The residual oil was easy to flow because of the lower IFT, thus improving the oil recovery rate [173].

Figure 6

(a) IFT values of SNP and synthesized PAAGS. (b) Variation in the IFT measured with Spinning drop technique (at 60°C) with NP size. (c) Effect of SNPs concentration and temperature on the IFT of crude oil-polymer-SNPs solution system at 5,000 ppm xanthan gum [172].

However, some scholars believed that there was no significant change in the reduction in IFT by coated polymers on NPs. It may be due to different experimental conditions [174]. Therefore, the ideal conditions and stability of the lowest interfacial tension of silica-based polymer NFs need further study.

3.4 Viscoelasticity

Viscoelasticity refers to the ability of a polymer solution to be both solid and liquid under specific flow conditions [175]. The phenomena related to viscoelastic properties in porous media mainly include (i) shear thickening, (ii) shear thinning, and (iii) elastic turbulence [176].

To understand viscoelasticity, we define the standard equation, where the shear viscosity equation is as follows [177]:

where η is the shear viscosity in Pa s , τ is the shear stress in Pa, and γ is the shear rate in s⁻¹.

The relaxation modulus is as follows [177]:

where G is the relaxation modulus in Pa.

The relaxation time λ is determined by elastic modulus and viscous modulus. When γ is less than 0.5, it is linear viscoelastic. And when γ is greater than 1, it is nonlinear viscoelasticity [178].

The linear viscoelastic equation can be defined as follows [179]:

where t is the time in s and t' is the past time running from the infinite past −∞ in s.

And the nonlinear viscoelastic equation is as follows (185):

where G is the relaxation modulus in Pa.

As shown in Figure 7, the polymer passed through the throat through elastic deformation. Due to viscoelasticity, displacement pressure can be better transferred in the flow process. In addition, viscoelasticity also had a drag effect on the residual oil at a formation dead angle. The viscoelasticity of silica-based polymer NFs improved scanning efficiency and oil recovery [119].

Figure 7

Viscoelastic polymer flooding mechanism [119].

Viscoelastic experiments by Hu et al. [60] verified that SiO₂ formed a high level of crosslinking. As a physical cross-linking agent, SiO₂ enhanced the network structure of ASM and improved its elasticity. Tang et al. [180] studied polymer/SiO₂ composite microspheres (PNSCMs) and found that with the increase in SiO₂, the elastic modulus (G′) and viscous modulus (G″) increased significantly. These results showed that the viscoelasticity of microspheres was enhanced. The following were the specific performances: (i) MPS-modified silica particles were uniformly dispersed in the polymer matrix as inorganic fillers, which increased the stress and energy required in the deformation process of the microspheres; (ii) SiO₂ produced a high crosslink density, forming a confined polymer region and introducing an energy dissipation mechanism; (iii) Slippage was decreased, and polymer chain movement was restrained. PNSCMs could thus easily enter the microchannel when there were large pressure differences, which improved the realization of reservoir depth control.

In the linear viscoelastic region, due to the interaction between silica and HPAM molecules, HPAM/NPs maintained a three-dimensional network structure under high temperature and high salt conditions. Adding fumed SNPs increased platform modulus and reduced critical strain. On the other hand, the incorporation of NPs reduced the critical strain amplitude and significantly changed the in-loop nonlinear behavior of the HPAM solution [181]. Furthermore, the mixed network formed by NPs enhanced the in-loop shear thickening response [182]. Since SNPs were cross-linked with HPAM to form a stable three-dimensional network structure, HPAM/NP had almost no relaxation time. At 85°C and 8 wt% NaCl, HPAM/NPs had elastic advantages [183].

3.5 Adsorption and porous media flow

Adsorption is the term used to describe the interaction of polymer molecules with rock surfaces [184]. In 1974, Hirasaki and Pope [185] studied the problems of polymer adsorption and porous media flow and concluded that the adsorption of polymers would reduce the permeability. In addition, the polymer retention mechanism was related to reservoir heterogeneity, showing different heterogeneity trends. The heterogeneous weak gel system was easy to retain in porous media and could establish impermeability in the medium [124]. Even for NPs with appropriate size and good stability, adsorption may hinder the transport of NPs. As a result, the adsorption of NPs and the transport mechanism in porous media are important challenges [186].

Songolzadeh and Moghadasi [187] pointed out that SiO₂ improved the flow behavior of polymers. However, the aggregation of nano-silica closed the pore throat and reduced the permeability, so it was necessary to modify nano-silica. Daneshmand et al. [88] used polyethylene glycol methyl ether and propyl chain to obtain PEG NPs. By adding the hydrophobic agent to SiO₂, the stability improved, and the retention of NP increased.

The results of static adsorption experiments revealed that the polymer containing nano-silica had less adsorption capacity than the general polymer on the surface of carbonate and sandstone, which eventually led to EOR [188]. As shown in Figure 8, the adsorption of a polymer solution containing SNPs was less than that of similar samples containing clay. Moreover, the adsorption rate of nano-silica polymer solution in sandstone was lower than that in carbonate. Because of pores and cracks, the adsorption capacity of the nano-silica polymer in carbonate was higher than that of sandstone [189]. Hydrophilic silica-nanoparticles had a high surface affinity with rock particles, thus reducing the adsorption of polymers in carbonate reservoirs [190]. However, some research results highlighted the complexity of the influence of dynamic factors (such as flow, permeability, etc.) and called in to question the validity of static measurements. More research is needed in this area [186].

Figure 8

SEM micrograms of the NP absorbed by the reservoir rock. Clay NP: (a) sandstone sample and (b) carbonate sample. SiO₂ NP: (c) sandstone sample and (d) carbonate sample [189].

Bessaies-Bey et al. [191] concluded that the adsorption of HPAM on silica surfaces formed hydrogen bonds, in which the silanol group played an important role. Due to the decrease in active adsorption sites, the adsorption of silica grafted HPAM was low. Liu et al. [96] studied SLPs synthesized with nano-silica and found that MW, polymer concentration, and sandstone permeability were the main factors affecting the flow behavior in porous media. When the ratio of the average pore size (rp) to hydrodynamic diameter (Hd) was less than 5.2, the effective pore size decreased due to polymer adsorption and bridging effect. It led to surface blockage and poor flow control in porous media. When rp/Hd was greater than 5.2, it had good liquidity performance. The designed SLP solution recovered 7.0% more than the same viscosity polymer solution. In addition, pH, ionic strength, and temperature affected the adsorption [192].

3.6 Emulsion stability

The emulsion which is also known as a suspension, is a metastable mixture of two immiscible liquids [193]. The formation of an emulsion mainly depends on the composition of crude oil [194]. It is vital that emulsion stability improves sweep efficiency [195]. The stability of the emulsion is relatively dependent on the droplet aggregation rate and the interfacial film strength [196,197]. Emulsion composed of NPs has noticeable temperature and salt tolerances. And due to their small particle size, NPs can move long distances in reservoirs [198]. The Pickering emulsion (SPN) prepared with silica and polymer had strong stability and improved recovery efficiency by about 24% [199]. Although NPs improved emulsion stability, the mechanism for EOR is still unclear [165].

Saha et al. [172] found that the diameter of oil droplets decreased after silica was added to xanthan gum. And the diameter of oil droplets decreased with the increase in SNPs concentration. When SNPs concentration was more than 0.3 wt%, the emulsion stability reached equilibrium. It was because the adhesion of silica prevented the aggregation of droplets [54]. On the other hand, the emulsion’s stability was increased by SNPs adhering to the oil–water interface [199].

Kumar et al. [199] synthesized SPN Pickering emulsion by using the base polymer carboxymethyl cellulose, SNPs (40 nm particle size), anionic surfactant sodium dodecylbenzene sulfonate, and light mineral oil (density 0.85 g/mL). The zeta potential of the emulsion was greater than −30 mV, indicating that its stability was improved compared with the emulsion prepared by surfactant-polymer or only surfactant. As shown in Figure 9, due to the added polymer, the stability of the emulsion at high temperatures and high pressure improved. The attraction of van der Waals force between polymer NPs and the formation of a layer due to electrostatic contributed to the interface stability [199,200]. Furthermore, at high shear rates, the emulsion aided the injection process and improved the injection rate [201]. When injected at a low shear rate, the viscosity value was required to be relatively stable to improve recovery [202].

Figure 9

Emulsion stabilization by adsorption of solid particles at oil–water interface [199].

The polymer-coated SNP formed a rigid layer on the surface of oil droplets, which effectively prevented the aggregation of oil droplets in the aqueous phase due to the steric hindrance mechanism [28]. More importantly, nanometer emulsion was easy to pass through micropores because the particles were so small, which greatly improved recovery [203]. Furthermore, the residual oil produced in the form of a water-in-oil emulsion and the decrease in interfacial tension created favorable conditions for the emulsion.

4.1 Overview of molecular simulation technology and macroscopic simulation

4.2 Mechanism of molecular dynamics simulation

Figure 10 is the general workflow of MD simulation, including initialization, energy minimization, equilibrium phase, and production phase [220–224]. In the first stage, we define preliminary information and simulation details [225]. Then the energy minimization step is to find the minimum energy level of the system [226]. In the equilibrium phase, the particles in the system are relaxed to the equilibrium state by changing the input and output energy [227,228]. Finally, in the production phase, trajectory data are collected and performance is analyzed [229].

1. Force field:

   The force field consists of potential energy and related parameters [230]. The position and molecular potential can be correlated by the following formula [228]:

   (7) ∇ E ( r 1 , r 2 , … , r N ) = m i d r i d t 2 ,

   where r i represents the position of atom i , E stands for the total potential energy, and m i denotes the atomic mass of atom i .

   The total energy of the system can be defined as follows [231]:

   (8) E Total = E bonded + E non − bonded ,

   where E Total stands for the total energy of the system, E bonded denotes the contribution of covalent energies, and E non − bonded represents the contribution of noncovalent energies.

   And, the E bonded and E non − bonded can be determined by the following formula:

   (9) E bonded = E bond + E angle + E torsion ,

   (10) E non − bonded = E electrostatic + E vanderWaals ,

   where E bonded stands for the potential energy due to the deformation of the bond length between two bonded atoms, E angle is the potential energy of angular motion between three bonded atoms which form two consecutive chemical bonds, and E torsion represents the potential energy due to the torsion of four atoms in a molecule.

   The widely used force fields are COMPASS, CHARMM, and GROMOS [232–234]. Each force field has its specific advantages and disadvantages, and the best one to use depends on the structure and the problems that need to be solved [235,236]. Verlet algorithm is the most widely used and most straightforward algorithm in molecular dynamics simulation [237,238]. According to the Taylor formula, the particle formula can be obtained as follows [237,239,240]:

   (11) r ( t + δ t ) = r ( t ) + d d t r ( t ) δ t + 1 2 ! d 2 d t 2 r ( t ) ( δ t ) 2 + ⋯ ,

   (12) r ( t − δ t ) = r ( t ) − d d t r ( t ) δ t + 1 2 ! d 2 d t 2 r ( t ) ( δ t ) 2 + ⋯ .

   According to equations (11) and (12), we can obtain

   (13) v ( t ) = d r d t = 1 2 δ t [ r ( t + δ t ) − r ( t − δ t ) ] ,

   (14) r ( t + δ t ) = − r ( t − δ t ) + 2 r ( t ) + d 2 d t 2 r ( t ) ( δ t ) 2 ,

   where r stands for the location of particles, v stands for the velocity of particles, δ t stands for a short interval.

2. Periodic boundary condition:

   In MD simulation, periodic boundary conditions are often used to calculate the length of the simulated box [241]. The periodic boundary assumption is that the particles are set in a simulation box [242]. The particles in the simulation box can leave from one side and enter from another measurement of the box, which makes the particles and density of the system remain unchanged. When calculating the force between particles in the box, the minimum image is often used to calculate the force between two particles [243]. However, when the periodic boundary conditions are used for simulation, the periodic mirror molecule should be consistent with its molecular motion [244]. Due to the introduction of a periodic boundary, there is an inevitable fluctuation for attributes that depend on long-term correlation.

3. Statistical ensembles:

   The statistical ensemble consists of many ideal states, which impose constraints on the system, such as temperature, pressure, total energy, and particle number [245]. The pressure, temperature, and total number of particles of the isobaric-isothermal (NPT) ensemble are fixed and are mainly used to analyze phase properties. However, the accuracy requirements for pressure and density are relatively high [246]. The microcanonical (NVE) ensemble has a fixed total volume, total energy, and total number of particles, which are primarily used to study the transport properties. However, due to the difficulty in fixing the energy state, there are certain limitations in the applications [231]. In addition, the total volume, temperature, and total number of particles in the canonical (NVT) ensemble are constant which is mainly used to evaluate the phase properties. But the system can only undergo heat exchange with the reservoir.

Figure 10

Schematic of the workflow of MD simulations.

4.3 Molecular simulation and macroscopic simulation applications

4.3.1 Mechanical properties of silica-based polymer NFs

El-hoshoudy et al. [58] optimized the COMPASS module with an energy of 0.001 kcal/mol and obtained the model of the silicon-co-acrylate composite material, as shown in Figure 11(a) and (b). After introducing the silane coupling agent, the total energy increased, which indicated that the silica incorporation improved the mechanical properties and rheology of the silicon-co-acrylate polymer. The addition of silica improved the mechanical properties by 31.6%, owing to the bonding strength formed by hydrogen bonds between different compositions [47]. Furthermore, the introduction of silane coupling agents increased Young’s modulus, which enhanced the mechanical properties and recovery of silicon-co-acrylate polymers in harsh reservoirs. When the silica content increased, the anisotropy and Young’s modulus of the system also increased [223]. The addition of silica increased the stiffness of the PVA/PAM but decreased its ductility [222].

Figure 11

(a) 3D-structure of silica-polyacrylate composite [58], (b) cellular structure of silica-polyacrylate composite [58], (c) 6PVA/6PAM/1 silica (6.9 wt% SiO₂ content) [223], and (d) 4PVA/4PVP/1 silica (10% SiO₂) [223].

Guo established the polymethylmethacrylate (PMMA)/SiO₂ composite model and PMMA/modified SiO₂ composite model. The research on the elastic modulus found that the elastic modulus of the PMMA/SiO₂ composite increased by 29.7% compared with that of PMMA polymer at room temperature. The elastic modulus of PMMA/SiO₂ composites with a 5% modification rate increased by 32.4%, while that of PMMA/SiO₂ composites with a 10% modification rate increased by 31.52%. This reveals that the elastic modulus of the unmodified polymer decreases with an increase in temperature. And the elastic modulus of low modification degree polymers is slightly higher than that of high modification degree polymers. The shear modulus study found that PMMA/SiO₂ was 18.32%. PMMA/SiO₂ with a 5% modification rate was 32.69%, and PMMA/SiO₂ with a 10% modification rate was 51.76%. It showed that the addition of SiO₂ made the performance better. And the higher the modification rate, the greater the improvement in shear modulus [247].

The layered model formed by octyltrimethoxysilane, vinyltrimethoxysilane-modified silica, and acrylic acid-acrylamide copolymer is shown in Figure 12(a) and (b). The diffusion coefficient and binding energy in Figure 12(a) were higher than that in Figure 12(b). It indicated that the solid interfacial binding force limited the flow of polymer chains, increasing the thermal stability of the composite microspheres [248].

Figure 12

(a) Octyltrimethoxysilane-modified silica and acrylic–acrylamide copolymer layered model [248], (b) vinyltrimethoxysilane-modified silica and acrylic–acrylamide copolymer layered model [248], (c) PAM/SiO₂ interface model [249], and (d) PAM/H₂O/SiO₂ interface model [249].